Mechanistic insight into the competition between interfacial and bulk reactions in microdroplets through N2O5 ammonolysis and hydrolysis

Reactive uptake of dinitrogen pentaoxide (N2O5) into aqueous aerosols is a major loss channel for NOx in the troposphere; however, a quantitative understanding of the uptake mechanism is lacking. Herein, a computational chemistry strategy is developed employing high-level quantum chemical methods; the method offers detailed molecular insight into the hydrolysis and ammonolysis mechanisms of N2O5 in microdroplets. Specifically, our calculations estimate the bulk and interfacial hydrolysis rates to be (2.3 ± 1.6) × 10−3 and (6.3 ± 4.2) × 10−7 ns−1, respectively, and ammonolysis competes with hydrolysis at NH3 concentrations above 1.9 × 10−4 mol L−1. The slow interfacial hydrolysis rate suggests that interfacial processes have negligible effect on the hydrolysis of N2O5 in liquid water. In contrast, N2O5 ammonolysis in liquid water is dominated by interfacial processes due to the high interfacial ammonolysis rate. Our findings and strategy are applicable to high-chemical complexity microdroplets.

notoriously tricky.This referee does not want to dig through the SIs to find the details.Some reasonable attempt has to be made to rule this out?If done correctly, MetaD vs Umbrella should not provide consistent results.
2. More importantly the 2D free energy surface of solvation + distance in the Galib-Limmer study seems to be a better coordinate for rates with a spot on committer distribution.The present study uses two distances and the authors should comment on this regarding the calculation of rates/commitors.3. QM/MM vs a single framwiork.If this is solvent mediated, then the QMMM may be problematic.QMMM is a decent framework and using QM water for the first 5 A seems reasonable, but this may more resemble a cluster in a dielectric.Did the authors test this?Meaning--doing the reactions with the cluster in an embedded dielectric?This would be an interesting test to ensure that the QMMM is indeed mimicking the condensed phase.This needs to be discussed in the main manuscript and perhaps further convincing tests that a the single QM framework vs the QMMM is equivalent for bulk studies.4. Zero K minima are interesting with the high-level theory but we are interested in relative fluctuations.This is what drives phenomena.
5. If it turns out that the duifference is solely due to the level of theory only I would be surprised.This should not change the qualitative outcome.If so, the authors must demonstrate this.The authors also must do a better job of conveying what is new and different to the Galib-Limmer study.At the moment there is nothing.6.The non-nutritive figures of trajectories and time series and snapshots need to be changed to something that teaches us about the process.7. Committors, etc for the dynamics would be interesting.This could lead to us understanding differences in rates.
8. If it is the two step mechanism vs. the Galib-Limmer mechanism--this needs to be clearly demonstrated beyond being stated.This would be an interesting result and Nature worthy.
One could focus the study about this and make it convincing.At present, this referee is left guessing as to what is different.The above issues need to be addressed in a thoughtful manner.Let me reiterate that I understand that this is not a referendum on the Galib-Limmer study--Nevertheless, there needs to be something to tell the reader what is different and what can be learned that is different.Just stating that the results are different in not sufficient.Reactions at interfaces are important.Seeking consistency between the two studies and telling the community in a constructive way the potential differences (appropriately caveated) would be be useful to provide a roadmap for other to continue and understand this important system.

Reviewer #4 (Remarks to the Author):
N2O5 is one of the key reservoir species in both stratospheric and tropospheric NOx cycles.
Its formation and removal rates thus affect both ozone levels, climate and air quality.In this manuscript, Y. G. Fang and co-workers use computational methods to assess the molecularlevel details of the main sink reaction of N2O5: uptake into the atmospheric aqueous phase (aqueous aerosols or cloud droplets), and subsequent formation of HNO3 (and possibly other co-products).The study reports two main findings: 1)in pure water droplets/aerosol, hydrolysis happens predominantly in the bulk phase rather than at the air-water interface as previously claimed; 2)in the presence of (some unspecified concentration of) ammonia, ammonolysis out-competes hydrolysis.While there are some issues/problems with the employed methods and the data analysis as discussed below, the overall methodology is probably sufficient at least for qualitative work (e.g. a comparison of the three channels discussed above), and the computational results are mostly reproducible with the given details (again, see below for some minor caveats).The work will thus certainly be of interest at least to atmospheric chemists working with molecular-level modelling.Assessing the broader significance of the work, for example to larger-scale modelling work concerning air quality, stratospheric ozone, or climate, is difficult to do based on the data presented so far.
While the information that N2O5 hydrolysis happens inside rather than at the surface of droplets is interesting, it is ultimately not particularly important -the net result is still that N2O5 is removed by hydrolysis.(This is reminiscent of the question of SO3 hydrolysis, where several studies have been published demonstrating that various molecules can catalyse the hydrolysis reaction.However, their impact and relevance is limited, as hydrolysis of SO3 to H2SO4 happens on sub-second timescales in any case, in almost any atmospheric conditions.)The second main result is potentially of greater relevance and impact, as it implies that the N2O5 removal rate might depend on the NH3 concentration, and/or possibly the aerosol or droplet composition and pH.(Please see also comment 6 below on quantifying the dependence of the removal rate on the NH3 concentration).However, even the "slower" quoted bulk hydrolysis rate of 2.3E-3 nanoseconds is quite fast -it implies that the lifetime of N2O5 in the bulk aqueous phase is less than a microsecond.Does it really matter if N2O5 is removed by ammonolysis in less than a nanosecond, or hydrolysis in less than a microsecond, if the net effect is in any case practically instantaneous N2O5 removal?
To my thinking, the answer may depend on the fate of the nitramide (NH2NO2) product formed in the ammonolysis pathway -is this molecule expected to live long enough to affect atmospheric chemistry (or to form more long-lived products other than HNO3)?If yes, how?
A quick literature search reveals relatively few studies on nitramide oxidation, or even nitramide reactions overall, and none about actual atmospheric oxidation.Tantalisingly, some of those (see e.g.https://pubs.acs.org/doi/10.1021/acs.est.6b04842 for an environmental chemistry study, albeit on a much larger compound) suggest N2O as a possible product.Even limited production of N2O from N2O5 in the atmospheric aqueous phase would certainly be "huge if true".I'm certainly interested in hearing the authors' reasoning (and possible speculations) here.

Specific comments:
1)The basis sets used in the "benchmark" geometry optimisations and energy calculations are rather modest for benchmarking purposes: 6-31+G** only has a single set of polarisation functions, while cc-pVTZ lacks any diffuse functions.Are the authors sure this is good enough for "benchmark quality"?
2)The three sets of numbers given in the first paragraph of the "Results and Discussion" section don't appear to match each other.For example, for the 1W-1 reaction, the energy barrier computed at "high levels of theory" is given as 14.3 to 16.8 kcal/mol.The rev-PBE barrier is then given as 8.6 kcal/mol.Finally, it is stated that this is "13.0 kcal/mol lower" than at the "benchmark" level.However, 8.6 is not 13 lower than 14. 3-16.8.The same applies to all the three other reactions -the quoted difference does not match the two previous numbers.Please clarify this.
3)I don't understand how Figure 1b and d can be interpreted to suggest that "revPBE performed the best".Especially for the ammonolysis reaction, revPBE performs very poorly, much worse than B3LYP, PBE0 or M02X, all of which are methods with roughly similar computational expense.(B2PLYP is much more expensive.)Is the argument here that revPBE is somehow a "low-level" method, while e.g.B3LYP is "high level"?Are the red columns in the figure supposed to be "low level", and the blue columns "high"?This division seems arbitrary and even incorrect, and even if it were true, revPBE is not really much better than the other "red" methods (which are all atrociously bad).1b and d correspond to the methods actually used in the QM/MM simulations (BPE-D3/DZVP-MOLOPT-SR and PBE0-D3/DZVP, according to the methods -section)?If yes, please label it accordingly -if no, please redo the calculations and include this method in the figure!5)Please explain from which data the transition-state theory rates are computed.I assume it is the PBE0-D3/DZVP data in the "high-level" QM/MM simulations?Given the rather large differences between PBE and CCSD(T) in Figures 1b and 1d, how reliable should the absolute rates be considered?Should they perhaps be reduced by some correction factor proportional to exp(-dE/RT), where dE is the difference in barrier heights between the methods?(Note that the answer to the previous question may render this question either more or less relevant.)

4)Do any of the entries in Figures
6)The hydrolysis rate is expressed in terms of a unimolecular rate coefficient (in units of 1/ns).While the reaction between N2O5 and H2O is of course bimolecular, in an aqueousphase (bulk or interface) context this is appropriate: the concentration of water is after all close to constant (even in relatively concentrated solutions), and it makes sense to implicitly include it in the rate coefficient.However, for ammonolysis this is not the case -the rate at which N2O5 is ammonolysed will certainly depend on the ammonia concentration, so giving one single pseudo-unimolecular number is meaningless.Please provide instead a figure or table of the pseudo-unimolecular ammonolysis rate as a function of the liquid-phase ammonia concentration, or even the gas-phase ammonia concentration.The latter actually becomes an interesting exercise, as the [NH3]aq depends not only on p_NH3 but also on pH -unless also NH4+ ions can ammonolyse N2O5?As a side note, the results would imply a possible pH -dependence of the N2O5 uptake coefficient, which would be intriguing, albeit with two caveats: 1)also the hydrolysis lifetime is so short that this dependence may not matter; and 2)just like in the case of SO3 mentioned above, it may well turn out that aqeuous-phase N2O5 destruction is catalysed by many different species, including both acidic and basic molecules.(The latter argument is certainly beyond the scope of the present manuscript, I'm just raising the issue as something the authors might want to look at later).
7)The authors are apparently comparing their pure-water uptake coefficients to measurements done for ammonium sulfate and bisulfate particles (discussion around Figure 6).However, their central argument in this study is that ammonia affects the uptake process!Does this not invalidate the comparison?8)Please explain a bit more what the transmission coefficient k(t) in 1 accounts for.Also, what does the "(t)" notation here mean -how is the coefficient time-dependent?

Reviewer #1
In this study, Fang et al. perform ab initio molecular dynamics simulations at the level of density functional theory with hybrid density functional to simulate the hydrolysis and ammonolysis of N2O5 in a bulk aqueous solution and at the air-water interface.They provide their gas-phase calculations as a rationale for using hybrid density functional.They use stepwise multi-subphase space metadynamics (SMS-MetaD) to identify reaction mechanisms and estimate the free energy barriers of the two reactions.
The main contribution of this study is the observation of the stepwise ionic mechanisms in N2O5 hydrolysis, as well as the first observation of N2O5 ammonolysis under aqueous solvation at a molecular level.The calculations suggest that hydrolysis in the bulk is much more significant than at the air-water interface.However, the fast ammonolysis at the airwater interface might play an essential role in the reactive uptake of N2O5 by atmospheric aerosols.
The manuscript is well-written and the results are novel and interesting enough to deserve publication in Nature Communication.However, there are several issues that the authors need to address before I can recommend the publication of this work.

Author response:
We appreciate the reviewer for the positive evaluation of our work and the constructive comments that helped to improve the clarity of the manuscript.We have carefully considered these suggestions and are committed to addressing the following issues to meet the standards of Nature Communications.

Reviewer #1 Major Comments:
1) The competition between interfacial and bulk processes is the main objective of this study.However, ammonolysis is only studied at the air-water interface.The authors might need to explain the reasons for not performing ammonolysis in bulk, as there are no bulk data to compare with the ammonolysis rate at the air-water interface.
Author response: We thank the reviewer for the comment.In this study, we did not study the ammonolysis in bulk for two reasons: 1).As shown in supplementary Fig. 1, both N2O5 and NH3 have interfacial affinity properties, which means that they are prone to collisions and reactions at the air-water interface.
2).The kinetics of N2O5 ammonolysis reaction are exceptionally rapid, resulting in the N2O5 ammonolysis reaction occurring before N2O5 diffuses into the bulk phase.Indeed, the reactodiffusive length is given by the following equation: where Daq is the diffusion coefficient and k is the pseudo first-order rate constant.Our calculations show that the lifetime of ammonolysis is ~9 ps.On the other hand, the diffusion coefficient is about 10 -5 cm 2 /s, and the reacto-diffusive length is calculated to be about 0.09 nm.Therefore, the reaction should be completed at the interface.Based on the reviewer's comment, we have made corresponding changes in the revised manuscript.
2) The authors need to clarify how the air-water interface is defined, as represented by the shaded areas in Fig. S1.

Author response:
We thank the referee for the comment.In this study, we use the widely accepted 10-90 thickness to define the air-water interface.Specifically, the air-water interface is defined as the region between 90 and 10% of the bulk density, which has been widely adopted (J.Chem.Phys.102, 4574-4583 (1995)).Based on the reviewer's comment, we have clarified how to define the air-water interface in the revised manuscript.
3) Gas-phase calculations suggest that it is necessary to use hybrid functionals to obtain reaction barriers reasonably close to those computed by coupled-clusters.However, metadynamics simulations in condensed phase are performed with van der Waals corrected functionals (PBE-D3 in step 1 and PBE0-D3 in step 2).While it is clear that vdW corrections are necessary to represent the structure of water, what can one expect about the effect of D3 correction on the reaction barriers?The functional used in the condensed phase calculations should be also benchmarked in gas phase.
Author response: We thank the referee for this suggestion.Following the suggestion, we investigate the effect of D3 correction on the reaction barriers.Fig. R1 shows the reaction energy barriers of N2O5 hydrolysis for different mechanisms in the gas phase calculated using the PBE0 functional with and without D3 correction.Apparently, the D3 correction has little effect on the hydrolysis reaction of N2O5 in the gas phase.Author response: We thank the referee for the comment.The selection of the PBE0-D3 functional is based on a balance between computational efficiency and accuracy.We calculated the reaction energy barriers of N2O5 hydrolysis for different mechanisms in the gas phase using revPBE0-D3 and PBE0-D3 functionals.As shown in Fig. R2, the two quantum chemical methods give almost identical energy barriers (the difference in energy barriers is less than 10%).On the other hand, computational efficiency is also crucial.According to our test, PBE0-D3 is 2-3 times more computationally efficient than revPBE0-D3.Therefore, although revPBE0-D3 may perform better in characterizing structural and thermodynamic properties of water, we chose PBE0-D3 as the more suitable option for our research.Author response: We thank the referee for the comment.Standard conventional AIMD simulations using high-level quantum chemical methods (e.g.PBE0-D3) to explore the reaction of N2O5 at the air-water interface and inside the bulk are virtually impossible.To overcome the difficulties, we performed QM/MM MD simulations using our developed SMS-MetaD method 1 to simulate the reaction of N2O5 in this study.We performed two-step MetaD simulations, In the first step, MetaD-biased QM/MM MD simulations with a large QM region, which comprises ~100 atoms, were performed at the PBE-D3/DZVP level of theory to identify free energy pathways (FEPs).Unlike the adaptive QM/MM simulations, the oxygen atoms in the MM region were frozen in position to prohibit the exchange of QM and MM solvent molecules, while the hydrogen atoms of water in MM region and all atoms in the QM region were free to move.To ensure that the oxygen atom positions in the MM region were reasonable, we ran 2.0 ns classical MD simulations prior to the QMMM dynamics simulations.
A similar strategy has been adopted previously. 2-3In the second step, high-level QM/MM MD simulations with a small QM region.The QM method at the PBE0-D3/DZVP level of theory was used to depict the molecules participating in chemical reactions that contained the N2O5 moving a gaseous N2O5 into liquid water.The free energy exhibits a global minimum centered at the air-water interface, and this global minimum relative to the gas phase (ΔFa = -3.5 kcal/mol) corresponds to an interfacial adsorption free energy.Moreover, the difference between the free energy of N2O5 in bulk water and that in gas phase (ΔFs = -1.5 kcal/mol) is defined as the solvation free energy for the gasous N2O5.Apparently, the calculated ΔFa agrees very well with the ΔFa obtained using the many body potential (ΔFa = -3.7 kcal/mol), which was parameterized from coupled-cluster calculations, and outperforms that calculated using the neural network potential (ΔFa = -2.7 kcal/mol).For ΔFa, although the value calculated by QM/MM is somewhat higher than the one calculated using the many body potential (ΔFs = -2.7 kcal/mol), it is almost the same as the one calculated based on the neural network potential (ΔFa = -1.5 kcal/mol).These results validate the effectiveness of the QM/MM method in studying the N2O5 reaction.Minor Comments: 1) It would be appropriate to add "D3" to the method used in the previous study by Galib et al., i.e., revPBE-D3/MOLOPT-DZVP, since the authors have been indicating the use of the D3 dispersion in their methods.
Author response: We thank the referee for the suggestion.We have added "D3" to the method in the work conducted by Galib et al. in the revised manuscript.
2) Under Fig. 1, the descriptions and the Roman numbers in the parentheses do not match.
Author response: Thanks!We have corrected the descriptions under Fig. 1 accordingly in the revised manuscript.
3) Line 156, the barriers in the gas phase are determined to be 23.0 kcal/mol and 31.8 kcal/mol, respectively, as shown in Fig. 3. Why would the barriers involving additional water challenged the conclusions of the Galib-Limmer study.Note that Galib and Limmer are also authors of the paper.They suggested that "The disagreement with respect to the neural network model could likely be a failure of the density functional used in the training data".This inspired us to use higher quality functionals to investigate the reactive uptake of N2O5 by atmospheric aerosol.
To address the concerns of the referee, further simulations were conducted to investigate the reasons behind the differences, which are discussed in the revised manuscript.
Reviewer #2 Major Comments: 1) Galib and Limmer used umbrella sampling.This study metadynamics.MetaD is notoriously tricky.This referee does not want to dig through the SIs to find the details.Some reasonable attempt has to be made to rule this out?If done correctly, MetaD vs Umbrella should not?? provide consistent results.consistent results.comparable accuracy with respect to the coupled cluster reference data it was parameterized.
Their calculations show that the evaporation rate is very slow compared to the adsorption rate with "corresponding higher accommodation coefficient relative to the previous neural network model study" (Galib-Limmer's study).In addition, by solving the reaction-diffusion equation, they found that interfaical reactivity "accounts for at most 20%", whereas Galib-Limmer's study estimated that almost 100% reactions occurred at the air-water interface.They suggested that "The disagreement with respect to the neural network model could likely be a failure of the density functional used in the training data".This inspired us to use higher quality functionals to investigate the reactive uptake of N2O5 by atmospheric aerosol.
In this work, we have developed a strategy to simulate reactions at the air-water interface and in bulk water using high quality functionals.Our approach successfully identified different mechanisms of N2O5 hydrolysis at the air-water interface and in bulk water, such as molecular mechanisms and ionic mechanisms.Additionally, we confirmed for the first time the existence of a stepwise ionic mechanism.Using SMS-MetaD method combined with QM/MM MD simulations, we obtained the free energy profiles for N2O5 hydrolysis via different mechanisms.
In agreement with Cruzeiro et al. but different from Galib-Limmer's study, most of the hydrolysis is predicted to take place in bulk water.Using the resistor model, we predicted the variation of the reaction uptake coefficients γ of N2O5 in pure water as a function of aerosol particle radius (Rp).As the particle radius increases from 40 nm to 130 nm, γ increases from 0.011~0.047to 0.023~0.067,which is in good agreement with experimental results.Finally, we have investigated for the first time the ammonolysis of N2O5 in liquid water, and our calculations show that, unlike the hydrolysis process, the interfacial process dominate the ammonolysis process due to the high interfacial ammonolysis rate.We have discussed the novelties and differences of our work compared to the Galib-Limmer's study in the revised manuscript.
6) The non-nutritive figures of trajectories and time series and snapshots need to be changed to something that teaches us about the process.
Author response: We thank the referee for the comment.We have modified Fig. 2 and Fig. 5 in the revised manuscript to improve its clarity.
7) Committors, etc for the dynamics would be interesting.This could lead to us understanding differences in rates.

Author response:
We thank the referee for the suggestion.As the ionic mechanism governed the N2O5 hydrolysis reaction in liquid water, we have analysed transition states for N2O5 hydrolysis via ionic mechanism.Specifically, we investigated 30 configurations belonging to the constrained ensemble with reaction coodrinate (RC) ranges from -0.025 to 0.025.The committors of configurations are narrowly distributed around 0.5 (Fig. R8), indicating that the transition state criterion used is good.One could focus the study about this and make it convincing.
Author response: We thank the referee for the comment.The stepwise ionic hydrolysis mechanism is indeed intriguing and has never been reported in the literature before.However, the difference between our calculations and Galib-Limmer's study lies mainly in the level of theory used.In the study, we obtained the free energy profiles for N2O5 hydrolysis via different mechanisms and showed that the calculated free energy barrier at the air-water interface and in bulk water are in the order of ionic mechanism > molecular mechanism ≈ stepwise ionic mechanism and molecular mechanism > stepwise ionic mechanism > ionic mechanism, respectively.These calculations suggest that stepwise ionic and molecular mechanisms play a major role in the N2O5 hydrolysis reaction at the air-water interface, whereas the ionic mechanism governed the N2O5 hydrolysis reaction in bulk water.
We would like to point out that our calculations explain the conflicting conclusions reached by Galib-Limmer's study (Science 371, 921-925 (2021)) and their collaborative research.(Nat.Commun.13, 1266 (2022)) In addition, we provide a quantitative understanding of the uptake mechanism underlying the reactive of N2O5 into aqueous aerosols.More importantly, the strategy and framework developed in this study could have extensions to microdroplets with high chemical complexity.9) At present, this referee is left guessing as to what is different.The above issues need to be addressed in a thoughtful manner.Let me reiterate that I understand that this is not a referendum on the Galib-Limmer study--Nevertheless, there needs to be something to tell the reader what is different and what can be learned that is different.Just stating that the results are different in not sufficient.Reactions at interfaces are important.Seeking consistency between the two studies and telling the community in a constructive way the potential differences (appropriately caveated) would be useful to provide a roadmap for other to continue and understand this important system.
Author response: We thank the referee for the comment.The reactive uptake of N2O5 by aqueous aerosol has long been of particular interest.Galib and Limmer first used neural network potentials to theoretically investigate the reactive uptake of N2O5 into an aqueous aerosol.They estimated a reactive uptake coefficient (γ) of 0.6 based the widely used resistor model, which is an order of magnitude higher than the experimentally derived coefficients (ranging from 0.04 to 0.06).To resolve the inconsistency, they assumed that the evaporation was barrierless and proposed that the uptake was dominated by interfacial processes.
However, later MD simulations using MB-nrg potentials challenged the conclusions of the Galib-Limmer study.Note that Galib and Limmer are also authors of the paper.They found that interfaical reaction "accounts for at most 20%", and "most of the hydrolysis is predicted to take place in bulk water".They suggested that "The disagreement with respect to the neural network model could likely be a failure of the density functional used in the training data".This inspired us to use higher quality functionals to investigate the reactive uptake of N2O5 by atmospheric aerosol.
Our calculations using high quality functionals give an explanation for the conflicting conclusions reached by Galib-Limmer's study and their collaborative research.Note that the uptake coefficient corresponding to the hydrolysis reaction rates estimated using the widely used resistor model are in good agreement with the experimental data.In addition, we provide a quantitative understanding of the uptake mechanism underlying the reactive of N2O5 into aqueous aerosols.More importantly, the strategy and framework developed in this study could used to study other systems with high quality functionals.

Reviewer #3
N2O5 is one of the key reservoir species in both stratospheric and tropospheric NOx cycles.
Its formation and removal rates thus affect both ozone levels, climate and air quality.In this manuscript, Y. G. Fang and co-workers use computational methods to assess the molecularlevel details of the main sink reaction of N2O5: uptake into the atmospheric aqueous phase (aqueous aerosols or cloud droplets), and subsequent formation of HNO3 (and possibly other co-products).
The study reports two main findings: 1) in pure water droplets/aerosol, hydrolysis happens predominantly in the bulk phase rather than at the air-water interface as previously claimed; 2) in the presence of (some unspecified concentration of) ammonia, ammonolysis outcompetes hydrolysis.While there are some issues/problems with the employed methods and the data analysis as discussed below, the overall methodology is probably sufficient at least for qualitative work (e.g. a comparison of the three channels discussed above), and the computational results are mostly reproducible with the given details (again, see below for some minor caveats).
The work will thus certainly be of interest at least to atmospheric chemists working with molecular-level modelling.Assessing the broader significance of the work, for example to larger-scale modelling work concerning air quality, stratospheric ozone, or climate, is difficult to do based on the data presented so far.While the information that N2O5 hydrolysis happens inside rather than at the surface of droplets is interesting, it is ultimately not particularly important -the net result is still that N2O5 is removed by hydrolysis.(This is reminiscent of the question of SO3 hydrolysis, where several studies have been published demonstrating that various molecules can catalyse the hydrolysis reaction.However, their impact and relevance is limited, as hydrolysis of SO3 to H2SO4 happens on sub-second timescales in any case, in almost any atmospheric conditions.)The second main result is potentially of greater relevance and impact, as it implies that the N2O5 removal rate might depend on the NH3 concentration, and/or possibly the aerosol or droplet composition and pH.(Please see also comment 6 below on quantifying the dependence of the removal rate on the NH3 concentration).However, even the "slower" quoted bulk hydrolysis rate of 2.3E-3 nanoseconds is quite fast -it implies that the lifetime of N2O5 in the bulk aqueous phase is less than a microsecond.Does it really matter if N2O5 is removed by ammonolysis in less than a nanosecond, or hydrolysis in less than a microsecond, if the net effect is in any case practically instantaneous N2O5 removal?
To my thinking, the answer may depend on the fate of the nitramide (NH2NO2) product formed in the ammonolysis pathway -is this molecule expected to live long enough to affect atmospheric chemistry (or to form more long-lived products other than HNO3)?If yes, how?
A quick literature search reveals relatively few studies on nitramide oxidation, or even nitramide reactions overall, and none about actual atmospheric oxidation.Tantalisingly, some of those (see e.g.https://pubs.acs.org/doi/10.1021/acs.est.6b04842 for an environmental chemistry study, albeit on a much larger compound) suggest N2O as a possible product.Even limited production of N2O from N2O5 in the atmospheric aqueous phase would certainly be "huge if true".I'm certainly interested in hearing the authors' reasoning (and possible speculations) here.
Author response: We appreciate the reviewer for the thorough and insightful comments on our manuscript.Over the past few decades, the reactive uptake of N2O5 on aerosols has been widely considered one of the most influential processes in heterogeneous chemistry.In this study, in addition to exploring the reaction kinetics of the hydrolysis and ammonolysis of N2O5 at the air-water interface and in bulk water, we present a practical framework for studying chemical reactions at the air-water interface, a key reaction site in the atmosphere, which is equally important.
In addition, we would like to point out that the quantitative picture of the uptake mechanisms has long been of particular interest.The reactive uptake of N2O5 into an aqueous aerosol was first investigated by Galib and Limmer using neural network potentials.They estimated a reactive uptake coefficient (γ) of 0.6 based on the widely used resistor model, (Science 371, 921-925 (2021)) which is an order of magnitude higher than experimentally derived coefficients (ranging from 0.04 to 0.06).To resolve the inconsistency, they assumed that the evaporation was barrierless and proposed that the uptake was dominated by interfacial processes.However, later MD simulations using MB-nrg potentials challenged the conclusions of the Galib-Limmer study.(Nat.Commun.13, 1266 (2022)) Note that Galib and Limmer are also authors of the paper.Our calculations using high quality functionals provide an explanation for this conflicting conclusion.
Finally, we have discussed the effect of NH3 concentration on the N2O5 ammonolysis and its impact on N2O generation in the revised manuscript.Relevant papers are also cited in the revised manuscript.
Furthermore, as pointed out by the reviewer, the descriptions of "high-level" and "lowlevel" are unclear and ambiguous.In the revised manuscript, we have replaced "low-level" with the terminology "generalized gradient approximation functionals (specifically BP86, BLYP, PBE, revPBE)" and "high-level" with "hybrid functionals (including B3LYP, PBE0, M06, B2PLYP, where B2PLYP represents a double-hybrid functional)".We have made corresponding changes in the revised manuscript. is the PBE0-D3/DZVP data in the "high-level" QM/MM simulations?Given the rather large differences between PBE and CCSD(T) in Figures 1b and 1d, how reliable should the absolute rates be considered?Should they perhaps be reduced by some correction factor proportional to exp(-dE/RT), where dE is the difference in barrier heights between the methods?(Note that the answer to the previous question may render this question either more or less relevant.) Author response: We thank the referee for the comment.The transition-state theory rates were computed using the PBE0-D3/DZVP-MOLOPT-SR data obtained from QM/MM simulations.The energy barriers (ΔEb) for the gas phase reactions calculated at PBE0/DZVP-MOLOPT-SR level are lower than those calculated at the CCSD(T)/aug-cc-PVTZ//PBE0/DZVP-MOLOPT-SR level.However, the performance of GGA functionals is very poor, while hybrid functionals perform much better than GGA functionals.Considering that it is impossible to use the CCSD(T) functional in QM/MM MD simulations because of the high computational cost, we used the PBE0 functional.
It is noteworthy that the difference in ΔEb between the gas phase reactions calculated at PBE0/DZVP-MOLOPT-SR level and those calculated at the CCSD(T)/aug-cc-PVTZ//PBE0/DZVP-MOLOPT-SR level decreases with the increase of water molecules.
Specifically, for reactions in which an H group of H2O is attached to the terminal oxygen atom of O2NONO2, i.e., pathways 1W-1 and 2W-1, as the number of water molecules increases from one to two, the difference in ΔEb between the gas phase reactions calculated at PBE0/DZVP-MOLOPT-SR level and those calculated at the CCSD(T)/aug-cc-PVTZ//PBE0/DZVP-MOLOPT-SR level decreases from 5.3 to 4.3 kcal/mol.It is expected that the hydrolysis reaction does not require any correction factor due to the large number of water molecules present in liquid water.In fact, the reactive uptake coefficient predicted using the uncorrected transition-state theory rates agrees well with experimental results.
6) The hydrolysis rate is expressed in terms of a unimolecular rate coefficient (in units of 1/ns).
While the reaction between N2O5 and H2O is of course bimolecular, in an aqueous-phase (bulk or interface) context this is appropriate: the concentration of water is after all close to constant (even in relatively concentrated solutions), and it makes sense to implicitly include it in the rate coefficient.However, for ammonolysis this is not the case -the rate at which N2O5 is ammonolysed will certainly depend on the ammonia concentration, so giving one single pseudo-unimolecular number is meaningless.Please provide instead a figure or table of the pseudo-unimolecular ammonolysis rate as a function of the liquid-phase ammonia concentration, or even the gas-phase ammonia concentration.The latter actually becomes an interesting exercise, as the [NH3]aq depends not only on p_NH3 but also on pH -unless also NH4 + ions can ammonolyse N2O5?As a side note, the results would imply a possible pH -dependence of the N2O5 uptake coefficient, which would be intriguing, albeit with two caveats: 1) also the hydrolysis lifetime is so short that this dependence may not matter; and 2) just like in the case of SO3 mentioned above, it may well turn out that aqeuous-phase N2O5 destruction is catalysed by many different species, including both acidic and basic molecules.(The latter argument is certainly beyond the scope of the present manuscript; I'm just raising the issue as something the authors might want to look at later).7) The authors are apparently comparing their pure-water uptake coefficients to measurements done for ammonium sulfate and bisulfate particles (discussion around Figure 6).However, their central argument in this study is that ammonia affects the uptake process!Does this not invalidate the comparison?
Fig. R1.Reaction energy barriers of N2O5 hydrolysis for different mechanisms in the gas phase calculated using the PBE0 functional with and without Grimme's D3 correction.

4 )
This is related to point 3. Previous works suggest that revPBE0-D3 provides the best representation of the structure and thermodynamics of water: is there a reason why the authors chose PBE0-D3 instead?Would one expect more accurate results using revPBE0-D3?

Fig
Fig. R5.(a) Typical snapshot structures taken from a QM/MM MD simulation of H2ONO2 + in bulk water.(b) Fraction of unreacted intermediate H2ONO2 + at the air-water interface or in bulk water as a function of simulation time.

Fig 2 )
Fig. R6.(a) Collective variable (CV) used in MetaD-biased AIMD simulation of N2O5 hydrolysis in bulk water.(b) Free energy profile for N2O5 hydrolysis in bulk water via the ionic mechanism simulated at the revPBE-D3 level of theory.

Fig. R7 .
Fig. R7.Free energy profile for N2O5 hydrolysis in bulk water via the ionic mechanism.MetaDbiased QM/MM MD simulation was performed.The QM part was simulated at the revPBE-D3 level of theory.

Fig. R8 .
Fig. R8.Distribution p(PB) of the probability for relaxing to the product within the constrained ensemble with RC ∈ [-0.025, 0.025].

4 ) 5 )
Do any of the entries in Figures 1b and d correspond to the methods actually used in the QM/MM simulations (PBE-D3/DZVP-MOLOPT-SR and PBE0-D3/DZVP, according to the methods -section)?If yes, please label it accordingly -if no, please redo the calculations and include this method in the figure!Please explain from which data the transition-state theory rates are computed.I assume it

Fig. R11 .
Fig. R11.Reaction rate of ammonolysis as a function of NH3 concentration.Upper and lower hydrolysis rate of N2O5 in liquid water are represented by dashed line.